# Can Light Waves Be Irregular?

From what I understand, electromagnetic radiation produced by an antenna is of the frequency that corresponds to the motion of the electrons moving around in the antenna. And I assume that the electrons in most set ups are generally vibrating in an approximately sinusoidal motion. But sinusoidal is definitely not the only periodic shape we can get electrons to vibrate in. We can have square waves or saw-tooth waves.

My question is is there any detectable difference or any additional theoretical property individual photons have that are produced or carry some other non-sinusoidal wave shape, or are photons' energy states fully described by their frequency?

To be clear I'm interested in the resulting properties of individual quanta and not statistical group properties.

• A multi-frequency broadcast (i.e. anything but a pure sine wave) will be made up of multiple photons. Jun 29, 2016 at 19:42
• Sunlight is pretty "irregular", if you want. It contains a wide range of frequencies and if you want to express that with quanta, you can do so using an ensemble. An individual quantum, OTOH, is just a single measurement on the field, so it can't tell you very much about the ensemble. That's no different from the classical case, where a single wave sample can't tell you much about the entire wave, either. Jun 29, 2016 at 19:50
• Remember that a square or saw-tooth wave is simply a combination of several sinusoidal waves at certain frequencies and amplitudes. When you get down to it, a (co)sine wave is really the only fundamental periodic shape you can have.
– Jim
Jun 29, 2016 at 20:01
• @Jim I understand that mathematically we can decompose (almost) any complex wave into an infinite Fourier series. But that fact alone doesn't necessarily imply that every physical electromagnetic wave isn't just approximated by but exactly equal to a finite combination of perfect (co)sine waves. Jun 29, 2016 at 20:07
• @JonCuster If that is true, would you mind expanding that into an actual answer with perhaps examples or sources? Jun 29, 2016 at 20:08